The Median Voter Theorem, Revisited

The median voter theorem states that if you assume the ideologies of the electorate can be represented as a one-dimensional space and there are only two parties/candidates in the election, each candidate will maximize their expected votes by adopting the policy preferences of the median voter. In that world the two candidates are indistinguishable and will each receive half of the votes of the electorate, at random. The prediction is that politicians will all gravitate toward the center and elections will be very close contests between two exceedingly similar options. I have always thought and continue to think that this theorem is at best useless and at worst a load of bull.

There are a lot of conditions that go into the Median Voter Theorem that don't hold in the real world. For starters you assume that we are restricted to a two-party system; new parties placing themselves at the 49th and 51st percentiles of the electorate would instantly obliterate the two median-voter parties, though you can argue that they, then, would become the two parties in turn and would move toward the center. It is also not clear that policy preferences can be meaningfully restricted to a single dimension without losing information crucial to vote-predicting; this gives rise to the probabilistic voting models, which can make similar unique-equilibrium predictions in multiple dimensions. But I think there's a deeper flaw here, and we can see it when we look at the two supposed "examples" of the MVT in action: the 2000 and 2004 Presidential elections.

The combined national popular vote margins of victories between the 2000 and 2004 Presidential elections was 3.0%. Of the 44 other Presidential elections since the national popular vote began in any meaningful sense, only 10 have had a margin smaller than that. These were very close elections. And it is very true that in 2000, at least, there were people who said that the two parties were converging on each other, that there was no difference between Bush and Gore. Put aside for the moment the fact that those people were always, and can now be plainly seen as having been, plainly wrong. Suppose that 2000 was the median voter theorem at work. What's the other prediction of that theorem? That all voters will vote at random, 50% heads, 50% tails. This is emphatically not born out by the evidence. Consider the percentage of the vote that Al Gore won among the following demographic groups:

Men: 42%     Women: 54%
Whites: 42%     Asians/Others: 55%     Hispanics: 62%      Blacks: 90%
Income under $15,000: 59%       Income over $100,000: 43%
Married Persons: 44%       Unmarried Persons: 57%
Union Members: 62%      Non-Union-Household Voters: 44%
GLBT Voters: 70%      Straight Voters: 47%
Gun Owners: 36%       Non-Gun Owners: 58%
Protestants: 42%      Catholics: 50%       Others/None: 62%      Jews: 79%
Conservative Christians: 18%       All others: 54%
Health Care Is Most Important Issue Voters: 64%      Taxes Are Most Important Issue Voters: 17%
Position on issues is more important: 55%       Leadership qualities are more important: 35%

I could go on. I could mention schisms from this same exit poll over specific issues like the environment, the role of government, etc. But you get the point. Voting patterns do not look random. Voters were not flipping a coin. The American electorate did not treat George W. Bush and Al Gore as being interchangeable (and good for them, especially since they voted for Gore!). So what's really going on here?

What I think the median voter theorem most misses is that political parties are not organizations which seek to win elections. They are organizations which seek to enact a public policy agenda. One of the most efficient ways to do that is to win elections, so that is what political parties spend most of their time doing. But the point is policy. In particular this is something that I think it's not surprising the economists who came up with this kind of political-economics voter choice theory missed. So what happens if we change the rules of the game? What if we now suppose that the players are two political parties who live on a one-dimensional axis of voter preferences that runs from, say, -1 to +1, but who themselves wish to be as close to, respectively, 1 and -1. And they also want to get elected. I'm not in the mood to do all the math of this right now, but my hunch is that there isn't one solution. But I'm pretty sure that the result is very, very different from the simple world of the median voter theorem. In particular, if you stipulate that parties get no satisfaction out of adopting the maximally-centrist position, then I think the equilibrium at the center breaks down: both parties are getting a payout of 0, so neither party has any incentive to stay, even if they have no incentive to leave either (since they will lose).

What I think will happen, and this has been my personal theory of partisan politics for a while, is that each party should adopt, over the long run, a position relative to its opponent which will give it an expected vote share of exactly 50%. The reasoning is fairly simple. If the position of one party is held constant, then there will be some point I* (equilibrium ideology) for the other party where it wins an expected share of one-half. If it is at this position, it has no incentive to become any more extreme, because it will lose if it does so, but it also has no incentive to become less extreme, because it will be enacting less of its agenda than maximally possible. (I think part of my assumption is that we are talking long-term and politics is kind of stochastic, so if the electorate is balanced 50/50 over the long run then the parties will win and lose an approximately equal number of elections.) That is to say, in a given election, if I lose by 3% then I wish I had been a little more moderate, but if I win by 7% I would like to have run on a more extreme platform: I still would have won, but I'd be able to enact a more sweeping agenda. Those surplus votes, in other words, are deeply inefficient.

The result is that my theory of partisan politics says that in an electoral system which requires candidates or parties to get approval from a majority of the electorate in any given election the only possible long-term equilibrium is two political parties each of which can make a viable appeal to the median voter of approximately the same strength as the other. Anything that shakes this model will simply return a new political system which meets that form. When an old party dies, a new party will arise, appealing to about 50% of the populace. When something alters the underlying political landscape, like, say, the country makes a decision to let black people vote, thus shifting the median voter, it won't be the case that the party most black people vote for wins every election going forward. Rather, that party will become a little more extreme and the other party will become a little more moderate, until the equilibrium is restored.

That's why I don't think the long-term result of the growth of Hispanics in this country is the "death" of the Republican Party. Maybe the Republican Party will die, though I doubt it will be that severe a shock. Given how institutionally dysfunctional that Party seems right now, I wouldn't be shocked if they spend a decade or so in the wilderness, unable to compete in the new world where you can't win nationally with just 35% of Hispanics. But eventually there will be some new party, possible still called the Republicans, that occupies an ideological space similar to today's GOP, but probably minus a lot of the anti-Hispanic xenophobia. And the Democrats will probably have moved a little to the left on Hispanic issues. And we'll be back at equilibrium. But it will be a new equilibrium, one that reflects the greater power of Hispanics.

So that's my version of the median voter theorem. No, political parties will not adopt the preferences of the median voter. But they will modulate their level of radicalism so that they are appealing to the median voter, and as few voters beyond that line as possible.
asd